Motion Planning for Multiple Autonomous Robotic Vehicles : an Application of Optimal Control Theory

Over the past few years we have witnessed an increasing use of multiple autonomous robotic vehicles in mission scenarios with increasing complexity and associated risks. The use of multiple vehicles provides a paradigm shift which involves using, instead of a large monolithic vehicle, a set of simpler vehicles, further enhancing flexibility and robustness against failures, while potentially lowering operation costs. For these reasons, there is great interest in developing efficient motion planning algorithms for cooperative missions. This thesis aims to contribute to the development of a new generation of systems for mission planning that incorporates in its formulation the dynamics of the vehicles. The first part describes the development of a trajectory generator for a single vehicle. For this, we make use of the so-called Projection Operator Approach, a mathematical tool proposed by Professor John Hauser of the Univ. Colorado, USA to solve optimal control problems. The generator synthesizes trajectories that minimize time or energy usage, avoiding, at the same time, collisions with fixed obstacles. The second part of the thesis focuses on the extension of the developed algorithm to the motion planing of multiple vehicles. We consider the case in which a group of vehicles is expected to reach a target position simultaneously, while minimizing expended energy and avoiding collisions with each other. Further, we consider the important case in which the vehicles need to move in formation. The overall system performance is assessed via computational simulations with realistic models of the Medusa marine vehicle. Keywords—Trajectory Generation, Collision Avoidance,TimeMinimal Optimization, Energy-Minimal Optimization, Projection Operator